Effect of price changes on the amount spent by consumers and revenue raised by firms, shown both in a diagram and as a calculation

0455 Allocation of Resources – Effect of Price Changes on Consumer Spending and Firm Revenue

Quick‑reference box – key terms

1. The role of markets in allocating resources

• Markets answer the three basic economic questions:

  1. What to produce?
  2. How to produce?
  3. For whom to produce?

• Buyers (consumers) express preferences through willingness to pay; sellers (producers) respond to profit opportunities.
• Prices act as signals that coordinate these decisions and allocate scarce resources efficiently (the “invisible hand”).

2. Demand

2.1 Definition & scope

Demand is the relationship between the price of a good and the quantity that consumers are willing and able to buy, ceteris paribus.

• Individual demand – one consumer’s schedule.
• Market demand – horizontal summation of all individual demand curves.

2.2 Movements vs. shifts

2.3 Diagram – right‑ward shift of demand

3. Supply

3.1 Definition & scope

Supply is the relationship between the price of a good and the quantity that producers are willing and able to sell, ceteris paribus.

3.2 Movements vs. shifts

3.3 Diagram – left‑ward shift of supply

4. Price determination – equilibrium

• At equilibrium, the quantity demanded equals the quantity supplied (Q_D=Q_S).
• The market‑clearing price (P_e) is the price at which this equality holds; the corresponding quantity is Q_e.
• If P > P_e → surplus → price falls; if P < P_e → shortage → price rises.

5. Causes of price changes

• Demand‑side causes – shift in demand (income, tastes, price of substitutes/complements, expectations, number of buyers).
• Supply‑side causes – shift in supply (input prices, technology, taxes/subsidies, expectations, number of sellers).
• Any shift alters the equilibrium price and quantity; the direction depends on whether the shift is in demand or supply.

6. Price elasticity of demand (PED)

6.1 Definition (mid‑point method – Cambridge requirement)

\[

\text{PED}= \frac{\displaystyle\frac{Q{2}-Q{1}}{(Q{1}+Q{2})/2}}

{\displaystyle\frac{P{2}-P{1}}{(P{1}+P{2})/2}}

\]

where subscript 1 = initial situation, subscript 2 = after the price change.

6.2 Interpretation of the coefficient

• Elastic demand (|PED| > 1) – quantity changes proportionally more than price.
• Unit‑elastic demand (|PED| = 1) – percentage change in quantity equals the percentage change in price.
• Inelastic demand (|PED| < 1) – quantity changes proportionally less than price.
• Perfectly elastic (|PED| = ∞) – horizontal demand curve.
• Perfectly inelastic (|PED| = 0) – vertical demand curve.

6.3 Determinants of PED (exam‑friendly checklist)

1. Availability of close substitutes – more substitutes → more elastic.
2. Proportion of income spent on the good – larger share → more elastic.
3. Nature of the good – luxuries are more elastic than necessities.
4. Time horizon – demand is more elastic in the long run.
5. Definition of the market – broader definition (e.g., “food”) → more inelastic.

7. Price elasticity of supply (PES) – brief overview

Calculated with the same mid‑point formula as PED. Supply is usually more elastic in the long run because producers can adjust plant size, labour, and technology.

8. Total expenditure (TE) and total revenue (TR)

Both are the product of price and quantity:

\[

\text{TE (or TR)} = P \times Q

\]

• For a consumer, TE is the amount spent on the good.
• For a firm, TR is the income earned from sales.

8.1 Relationship between price change, elasticity and TE/TR

9. Numerical illustration – IGCSE‑style example

Scenario: The price of petrol in Country X falls from \$1.20 per litre to \$1.00 per litre. Quantity demanded rises from 1 million litres to 1.3 million litres per month.

Interpretation: A 16.7 % fall in price leads to a 30 % rise in quantity demanded, giving |PED| = 1.8 (elastic). Total expenditure rises from \$1.2 m to \$1.3 m.

10. Diagrammatic representation of the total‑revenue test

1. Draw a single downward‑sloping demand curve labelled D. Divide it into three zones:

   • Upper‑left – elastic region (|PED| > 1)
   • Middle – unit‑elastic point (|PED| = 1)
   • Lower‑right – inelastic region (|PED| < 1)

2. Mark an initial price‑quantity pair (P₀, Q₀) on the elastic part. Draw a rectangle under the curve (height = P₀, width = Q₀) and label it “TR₀”.
3. Show a price fall to P₁ (still on the same demand curve) with the new quantity Q₁. Draw the second rectangle “TR₁”. Because the elastic region expands, TR₁ > TR₀.
4. Repeat the exercise on the inelastic part to illustrate that a price rise increases TR, while a price fall reduces TR.
5. Highlight the unit‑elastic point where the two rectangles have equal area – this is the point where TE/TR is unchanged.

11. Government policy – taxes and subsidies

• Specific tax on a good – shifts the supply curve upward by the amount of the tax.

  • If demand is inelastic, the tax raises the price paid by consumers only slightly, quantity falls little, and government revenue is relatively large.
  • If demand is elastic, the tax causes a large fall in quantity, consumer price rises little, and tax revenue is smaller.

• Subsidy to producers – shifts supply downward. The effect on market price and output follows the same logic: the larger the PED, the smaller the price change for consumers, but the larger the change in quantity.

12. Exam technique – meeting AO1, AO2 & AO3

AO1 – Knowledge & understanding

• State definitions of market, demand, supply, equilibrium, PED, PES, TE, TR.
• Recall the three elasticity categories and the “total‑revenue test”.

AO2 – Application & analysis

• Identify likely elasticity of a given good using the determinants checklist.
• Calculate PED (mid‑point method) from a data table.
• Predict the direction of change in TE/TR after a price change.
• Analyse a diagram showing movement along a demand curve and the associated revenue rectangles.
• Explain the impact of a tax or subsidy on price, quantity and government revenue.

AO3 – Evaluation

• Discuss limitations of the “total‑revenue test” (ceteris paribus, ignores income effects, short‑run vs long‑run).
• Weigh advantages and disadvantages of taxing an inelastic versus an elastic good.
• Consider how elasticity may change over time and how that alters revenue outcomes.

Command‑word reminders

13. Practice questions (with mark schemes)

1. MCQ (1 mark) – Which of the following goods is most likely to have an elastic demand?
   

   A. Salt B. Luxury sports cars C. Insulin D. Bread
   

   Answer: B (luxury good, many close substitutes).

2. Short answer (4 marks) – The price of cinema tickets falls from \$12 to \$10 and the quantity demanded rises from 1 000 to 1 300 tickets per week. Calculate the PED using the mid‑point method and state whether the demand is elastic, unit‑elastic or inelastic.
   

   Solution:
   

   \[

   \text{PED}= \frac{(1\,300-1\,000)/(1\,150)}{(10-12)/(11)}=

   \frac{300/1\,150}{-2/11}= \frac{0.2609}{-0.1818}= -1.44

   \]

   |PED| = 1.44 > 1 ⇒ demand is elastic. (4 marks: formula, substitution, calculation, interpretation.)

3. Data response (8 marks) – The table shows the effect of a 20 % price increase on three different goods. Use the data to calculate PED for each good, then explain which good would generate the greatest increase in total revenue after the price rise.
   

   Good	Initial price (P₁)	New price (P₂)	Initial Q (Q₁)	New Q (Q₂)
   A	\$5	\$6	200	180
   B	\$2	\$2.40	500	460
   C	\$10	\$12	80	70

   Solution outline (8 marks):

   • Calculate PED for each good (2 marks each). Example for Good A:
     

     \[

     \text{PED}_A= \frac{(180-200)/(190)}{(6-5)/(5.5)}= \frac{-20/190}{1/5.5}= -0.58

     \] (|PED| < 1, inelastic).

   • Identify that an inelastic demand means a price rise increases TR.
   • Compare the absolute values: Good A (|PED| ≈ 0.58) is most inelastic, so its TR rises the most.
   • State the conclusion and briefly link to the total‑revenue test.